100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Asilya Suleymanova

On the spectral geometry of manifolds with singularities
Thursday, 6 June, 2019 - 14:00
Résumé : 

In this talk, we consider the heat kernel of the Laplace-Beltrami operator on a Riemannian manifold. On any closed smooth Riemannian manifold the heat trace expansion gives some geometrical information such as dimension, volume and total scalar curvature of the manifold. On a manifold with conic singularities (if time permits, also on a manifold with two strata), we derive a detailed asymptotic expansion of the heat trace using the Singular Asymptotics Lemma of Jochen Brüning and Robert T. Seeley. Then we investigate how the terms in the expansion reflect the geometry of the manifold. Can one hear a singularity?

Thème de recherche : 
Théorie spectrale et géométrie
Salle : 
logo uga logo cnrs